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1.
A census of 4-valent half-arc-transitive graphs and arc-transitive digraphs of valence two : dedicated to Dragan Marušič on the occasion of his 60th birthday
Primož Potočnik, Pablo Spiga, Gabriel Verret, 2015, original scientific article

Abstract: A complete list of all connected arc-transitive asymmetric digraphs of in-valence and out-valence 2 on up to 1000 vertices is presented. As a byproduct, a complete list of all connected 4-valent graphs admitting a half-arc-transitive group of automorphisms on up to 1000 vertices is obtained. Several graph-theoretical properties of the elements of our census are calculated and discussed.
Keywords: graphs, digraphs, edge-transitive, vertex-transitive, arc-transitive, half arc-transitive
Published in RUP: 31.12.2021; Views: 799; Downloads: 16
.pdf Full text (370,47 KB)

2.
An alternate proof of the monotonicity of the number of positive entries in nonnegative matrix powers
Slobodan Filipovski, 2021, original scientific article

Keywords: digraphs, monotonicity, adjacency matrix
Published in RUP: 04.02.2021; Views: 834; Downloads: 28
.pdf Full text (265,78 KB)

3.
Digraphs with small automorphism groups that are Cayley on two nonisomorphic groups
Luke Morgan, Joy Morris, Gabriel Verret, 2020, original scientific article

Keywords: Cayley digraphs, Cayley index
Published in RUP: 17.06.2020; Views: 1560; Downloads: 38
.pdf Full text (396,72 KB)

4.
5.
Arc-transitive digraphs of given out-valency and with blocks of given size
Luke Morgan, Primož Potočnik, Gabriel Verret, 2019, original scientific article

Abstract: Given integers ▫$k$▫ and ▫$m$▫, we construct a ▫$G$▫-arc-transitive graph of valency ▫$k$▫ and an ▫$L$▫-arc-transitive oriented digraph of out-valency ▫$k$▫ such that ▫$G$▫ and ▫$L$▫ both admit blocks of imprimitivity of size ▫$m$▫.
Keywords: arc-transitive digraphs, Cayley digraphs, imprimitive digraphs
Published in RUP: 28.06.2019; Views: 1572; Downloads: 126
URL Link to full text

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7.
A note on a conjecture on consistent cycles
Štefko Miklavič, 2013, original scientific article

Abstract: Let ▫$\Gamma$▫ denote a finite digraph and let ▫$G$▫ be a subgroup of its automorphism group. A directed cycle ▫$\vec{C}$▫ of▫ $\Gamma$▫ is called ▫$G$▫-consistent whenever there is an element of ▫$G$▫ whose restriction to▫ $\vec{C}$▫ is the 1-step rotation of ▫$\vec{C}$▫. In this short note we provea conjecture on ▫$G$▫-consistent directed cycles stated by Steve Wilson.
Keywords: graph theory, digraphs, consistent directed cycles
Published in RUP: 15.10.2013; Views: 2540; Downloads: 123
.pdf Full text (229,03 KB)

8.
On Cayley digraphs on nonisomorphic 2-groups
István Kovács, Mary Agnes Milanič, 2012, original scientific article

Keywords: Cayley digraphs, isomorphisms, abelian groups, wreath products
Published in RUP: 15.10.2013; Views: 2867; Downloads: 209
URL Link to full text

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